Optimal longitudinal trajectory generation under varied lateral acceleration constraints

ABSTRACT

In one embodiment, a method, apparatus, and system for planning a trajectory for an autonomous driving vehicle (ADV) is disclosed. The operations comprise: receiving a plurality of optimization inputs, the plurality of optimization inputs comprising a trajectory time length, a time discretization resolution, an autonomous driving vehicle (ADV) starting state, a road shape function, a maximal jerk, and a maximal lateral acceleration; receiving a plurality of optimization constraints, the plurality of optimization constraints comprising constraints relating to the maximal jerk and the maximal lateral acceleration; receiving a cost function associated with an optimization objective, the cost function comprising a first term relating to cumulative jerk, a second term relating to an end longitudinal position, a third term relating to an end longitudinal speed, and a fourth term relating to an end longitudinal acceleration; generating a plurality of planned ADV states as optimization results with nonlinear optimization, wherein the optimization results minimize a value of the cost function; and generating control signals to control the ADV based on the plurality of planned ADV states.

TECHNICAL FIELD

Embodiments of the present disclosure relate generally to autonomous vehicles. More particularly, embodiments of the disclosure relate to planning a longitudinal trajectory under lateral acceleration constraints.

BACKGROUND

Vehicles operating in an autonomous mode (e.g., driverless) can relieve occupants, especially the driver, from some driving-related responsibilities. When operating in an autonomous mode, the vehicle can navigate to various locations using onboard sensors, allowing the vehicle to travel with minimal human interaction or in some cases without any passengers.

Motion planning and control are critical in autonomous driving. Longitudinal trajectories are trajectories that specify the movement of autonomous vehicles along the road/lane center line. Longitudinal trajectory generation is of great importance for many autonomous driving systems, e.g., adaptive cruise control systems. These autonomous driving systems typically deal with the in-lane driving scenarios, e.g., cruise to target speed, follow a lead vehicle, or stop at target point in the same lane. Several common factors, e.g., safety, comfort, time efficiency, must be considered in the trajectory generation process, making trajectory generation a difficult problem. Specifically, considering the shape of the road/lane, the autonomous vehicle must decelerate to a speed at curves to make a safe and comfortable ride, and accelerate to a desirable speed at the relatively straight road portion to be time efficient.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure are illustrated by way of example and not limitation in the figures of the accompanying drawings in which like references indicate similar elements.

FIG. 1 is a block diagram illustrating a networked system according to one embodiment.

FIG. 2 is a block diagram illustrating an example of an autonomous vehicle according to one embodiment.

FIGS. 3A-3B are block diagrams illustrating an example of a perception and planning system used with an autonomous vehicle according to one embodiment.

FIG. 4 is a diagram illustrating a vehicle pose under an SL-coordinate system under an XY plane according to one embodiment.

FIG. 5 is a block diagram illustrating various example components involved in the optimization process according to one embodiment.

FIG. 6 is a flowchart illustrating an example method for planning an optimal trajectory at an ADV according to one embodiment.

FIG. 7 is a block diagram illustrating a data processing system according to one embodiment.

DETAILED DESCRIPTION

Various embodiments and aspects of the disclosures will be described with reference to details discussed below, and the accompanying drawings will illustrate the various embodiments. The following description and drawings are illustrative of the disclosure and are not to be construed as limiting the disclosure. Numerous specific details are described to provide a thorough understanding of various embodiments of the present disclosure. However, in certain instances, well-known or conventional details are not described in order to provide a concise discussion of embodiments of the present disclosures.

Reference in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in conjunction with the embodiment can be included in at least one embodiment of the disclosure. The appearances of the phrase “in one embodiment” in various places in the specification do not necessarily all refer to the same embodiment.

According to some embodiments, a method, apparatus, and system for generating time optimal trajectories using optimization techniques that directly take the shape of the road/lane into account. In particular, a trajectory optimizer generates a plurality of planned autonomous driving vehicle (ADV) states with nonlinear optimization based on a plurality of optimization inputs, a plurality of optimization constraints, and a cost function. The planned ADV states may then be used to generate control signals to control the ADV.

In one embodiment, plurality of optimization inputs comprising a trajectory time length, a time discretization resolution, an ADV starting state, a road shape function, a maximal jerk (derivative of acceleration with respect to time), and a maximal lateral acceleration are received by the trajectory optimizer. A plurality of optimization constraints comprising constraints relating to the maximal jerk and the maximal lateral acceleration are received. A cost function associated with an optimization objective and comprising a first term relating to cumulative jerk and second, third, and fourth terms relating to an end longitudinal position, an end longitudinal speed, and an end longitudinal acceleration, respectively, is received. Thereafter, a plurality of planned ADV states are generated as optimization results with nonlinear optimization by the trajectory optimizer, wherein the optimization results minimize a value of the cost function. Control signals are then generated to control the ADV based on the plurality of planned ADV states.

In one embodiment, an SL-coordinate system comprising a longitudinal dimension and a lateral dimension is utilized, where the longitudinal dimension is along a tangential direction of a reference line, and the lateral dimension is perpendicular to the longitudinal dimension.

In one embodiment, each of the ADV starting state and the plurality of planned ADV states comprises a longitudinal pose, a longitudinal speed, and a longitudinal acceleration. In one embodiment, the road shape function comprises a sequence of spiral curves in the form of quartic polynomial functions. In one embodiment, the cost function further comprises a first weight associated with the first term, a second weight associated with the second term, a third weight associated with the third term, and a fourth weight associated with the fourth term.

In one embodiment, the plurality of planned ADV states correspond to time instants spaced by the time discretization resolution between a planning starting time and a planning ending time, and wherein the planning ending time is later than the planning starting time by the trajectory time length. In one embodiment, the plurality of optimization inputs further comprise a target ADV ending state.

Therefore, one embodiment of the disclosure is related to a trajectory optimizer that performs nonlinear optimization and generates planned ADV states that meet two optimization goals: 1) minimizing cumulative jerk, and 2) bringing the vehicle as close to the target end longitudinal position at the end of the trajectory time length as possible, or if no target end longitudinal position is specified, as far along the tangential direction of the reference line (i.e., the longitudinal dimension) as possible.

FIG. 1 is a block diagram illustrating an autonomous vehicle network configuration according to one embodiment of the disclosure. Referring to FIG. 1, network configuration 100 includes autonomous vehicle 101 that may be communicatively coupled to one or more servers 103-104 over a network 102. Although there is one autonomous vehicle shown, multiple autonomous vehicles can be coupled to each other and/or coupled to servers 103-104 over network 102. Network 102 may be any type of networks such as a local area network (LAN), a wide area network (WAN) such as the Internet, a cellular network, a satellite network, or a combination thereof, wired or wireless. Server(s) 103-104 may be any kind of servers or a cluster of servers, such as Web or cloud servers, application servers, backend servers, or a combination thereof. Servers 103-104 may be data analytics servers, content servers, traffic information servers, map and point of interest (MPOI) servers, or location servers, etc.

An autonomous vehicle refers to a vehicle that can be configured to in an autonomous mode in which the vehicle navigates through an environment with little or no input from a driver. Such an autonomous vehicle can include a sensor system having one or more sensors that are configured to detect information about the environment in which the vehicle operates. The vehicle and its associated controller(s) use the detected information to navigate through the environment. Autonomous vehicle 101 can operate in a manual mode, a full autonomous mode, or a partial autonomous mode. Hereinafter the terms “autonomous vehicle” and “autonomous driving vehicle” (ADV) may be used interchangeably.

In one embodiment, autonomous vehicle 101 includes, but is not limited to, perception and planning system 110, vehicle control system 111, wireless communication system 112, user interface system 113, infotainment system 114, and sensor system 115. Autonomous vehicle 101 may further include certain common components included in ordinary vehicles, such as, an engine, wheels, steering wheel, transmission, etc., which may be controlled by vehicle control system 111 and/or perception and planning system 110 using a variety of communication signals and/or commands, such as, for example, acceleration signals or commands, deceleration signals or commands, steering signals or commands, braking signals or commands, etc.

Components 110-115 may be communicatively coupled to each other via an interconnect, a bus, a network, or a combination thereof. For example, components 110-115 may be communicatively coupled to each other via a controller area network (CAN) bus. A CAN bus is a vehicle bus standard designed to allow microcontrollers and devices to communicate with each other in applications without a host computer. It is a message-based protocol, designed originally for multiplex electrical wiring within automobiles, but is also used in many other contexts.

Referring now to FIG. 2, in one embodiment, sensor system 115 includes, but it is not limited to, one or more cameras 211, global positioning system (GPS) unit 212, inertial measurement unit (IMU) 213, radar unit 214, and a light detection and range (LIDAR) unit 215. GPS system 212 may include a transceiver operable to provide information regarding the position of the autonomous vehicle. IMU unit 213 may sense position and orientation changes of the autonomous vehicle based on inertial acceleration. Radar unit 214 may represent a system that utilizes radio signals to sense objects within the local environment of the autonomous vehicle. In some embodiments, in addition to sensing objects, radar unit 214 may additionally sense the speed and/or heading of the objects. LIDAR unit 215 may sense objects in the environment in which the autonomous vehicle is located using lasers. LIDAR unit 215 could include one or more laser sources, a laser scanner, and one or more detectors, among other system components. Cameras 211 may include one or more devices to capture images of the environment surrounding the autonomous vehicle. Cameras 211 may be still cameras and/or video cameras. A camera may be mechanically movable, for example, by mounting the camera on a rotating and/or tilting a platform.

Sensor system 115 may further include other sensors, such as, a sonar sensor, an infrared sensor, a steering sensor, a throttle sensor, a braking sensor, and an audio sensor (e.g., microphone). An audio sensor may be configured to capture sound from the environment surrounding the autonomous vehicle. A steering sensor may be configured to sense the steering angle of a steering wheel, wheels of the vehicle, or a combination thereof. A throttle sensor and a braking sensor sense the throttle position and braking position of the vehicle, respectively. In some situations, a throttle sensor and a braking sensor may be integrated as an integrated throttle/braking sensor.

In one embodiment, vehicle control system 111 includes, but is not limited to, steering unit 201, throttle unit 202 (also referred to as an acceleration unit), and braking unit 203. Steering unit 201 is to adjust the direction or heading of the vehicle. Throttle unit 202 is to control the speed of the motor or engine that in turn control the speed and acceleration of the vehicle. Braking unit 203 is to decelerate the vehicle by providing friction to slow the wheels or tires of the vehicle. Note that the components as shown in FIG. 2 may be implemented in hardware, software, or a combination thereof.

Referring back to FIG. 1, wireless communication system 112 is to allow communication between autonomous vehicle 101 and external systems, such as devices, sensors, other vehicles, etc. For example, wireless communication system 112 can wirelessly communicate with one or more devices directly or via a communication network, such as servers 103-104 over network 102. Wireless communication system 112 can use any cellular communication network or a wireless local area network (WLAN), e.g., using WiFi to communicate with another component or system. Wireless communication system 112 could communicate directly with a device (e.g., a mobile device of a passenger, a display device, a speaker within vehicle 101), for example, using an infrared link, Bluetooth, etc. User interface system 113 may be part of peripheral devices implemented within vehicle 101 including, for example, a keyboard, a touch screen display device, a microphone, and a speaker, etc.

Some or all of the functions of autonomous vehicle 101 may be controlled or managed by perception and planning system 110, especially when operating in an autonomous driving mode. Perception and planning system 110 includes the necessary hardware (e.g., processor(s), memory, storage) and software (e.g., operating system, planning and routing programs) to receive information from sensor system 115, control system 111, wireless communication system 112, and/or user interface system 113, process the received information, plan a route or path from a starting point to a destination point, and then drive vehicle 101 based on the planning and control information. Alternatively, perception and planning system 110 may be integrated with vehicle control system 111.

For example, a user as a passenger may specify a starting location and a destination of a trip, for example, via a user interface. Perception and planning system 110 obtains the trip related data. For example, perception and planning system 110 may obtain location and route information from an MPOI server, which may be a part of servers 103-104. The location server provides location services and the MPOI server provides map services and the POIs of certain locations. Alternatively, such location and MPOI information may be cached locally in a persistent storage device of perception and planning system 110.

While autonomous vehicle 101 is moving along the route, perception and planning system 110 may also obtain real-time traffic information from a traffic information system or server (TIS). Note that servers 103-104 may be operated by a third party entity. Alternatively, the functionalities of servers 103-104 may be integrated with perception and planning system 110. Based on the real-time traffic information, MPOI information, and location information, as well as real-time local environment data detected or sensed by sensor system 115 (e.g., obstacles, objects, nearby vehicles), perception and planning system 110 can plan an optimal route and drive vehicle 101, for example, via control system 111, according to the planned route to reach the specified destination safely and efficiently.

Server 103 may be a data analytics system to perform data analytics services for a variety of clients. In one embodiment, data analytics system 103 includes data collector 121 and machine learning engine 122. Data collector 121 collects driving statistics 123 from a variety of vehicles, either autonomous vehicles or regular vehicles driven by human drivers. Driving statistics 123 include information indicating the driving commands (e.g., throttle, brake, steering commands) issued and responses of the vehicles (e.g., speeds, accelerations, decelerations, directions) captured by sensors of the vehicles at different points in time. Driving statistics 123 may further include information describing the driving environments at different points in time, such as, for example, routes (including starting and destination locations), MPOIs, road conditions, weather conditions, etc.

Based on driving statistics 123, machine learning engine 122 generates or trains a set of rules, algorithms, and/or predictive models 124 for a variety of purposes. In one embodiment, algorithms 124 may include an optimization algorithm that generates optimal planned ADV states based on inputs, constraints, and a cost function. Algorithms 124 can then be uploaded on ADVs to be utilized during autonomous driving in real-time.

FIGS. 3A and 3B are block diagrams illustrating an example of a perception and planning system used with an autonomous vehicle according to one embodiment. System 300 may be implemented as a part of autonomous vehicle 101 of FIG. 1 including, but is not limited to, perception and planning system 110, control system 111, and sensor system 115. Referring to FIGS. 3A-3B, perception and planning system 110 includes, but is not limited to, localization module 301, perception module 302, prediction module 303, decision module 304, planning module 305, control module 306, routing module 307, trajectory optimizer 308.

Some or all of modules 301-308 may be implemented in software, hardware, or a combination thereof. For example, these modules may be installed in persistent storage device 352, loaded into memory 351, and executed by one or more processors (not shown). Note that some or all of these modules may be communicatively coupled to or integrated with some or all modules of vehicle control system 111 of FIG. 2. Some of modules 301-308 may be integrated together as an integrated module.

Localization module 301 determines a current location of autonomous vehicle 300 (e.g., leveraging GPS unit 212) and manages any data related to a trip or route of a user. Localization module 301 (also referred to as a map and route module) manages any data related to a trip or route of a user. A user may log in and specify a starting location and a destination of a trip, for example, via a user interface. Localization module 301 communicates with other components of autonomous vehicle 300, such as map and route information 311, to obtain the trip related data. For example, localization module 301 may obtain location and route information from a location server and a map and POI (MPOI) server. A location server provides location services and an MPOI server provides map services and the POIs of certain locations, which may be cached as part of map and route information 311. While autonomous vehicle 300 is moving along the route, localization module 301 may also obtain real-time traffic information from a traffic information system or server.

Based on the sensor data provided by sensor system 115 and localization information obtained by localization module 301, a perception of the surrounding environment is determined by perception module 302. The perception information may represent what an ordinary driver would perceive surrounding a vehicle in which the driver is driving. The perception can include the lane configuration, traffic light signals, a relative position of another vehicle, a pedestrian, a building, crosswalk, or other traffic related signs (e.g., stop signs, yield signs), etc., for example, in a form of an object. The lane configuration includes information describing a lane or lanes, such as, for example, a shape of the lane (e.g., straight or curvature), a width of the lane, how many lanes in a road, one-way or two-way lane, merging or splitting lanes, exiting lane, etc.

Perception module 302 may include a computer vision system or functionalities of a computer vision system to process and analyze images captured by one or more cameras in order to identify objects and/or features in the environment of autonomous vehicle. The objects can include traffic signals, road way boundaries, other vehicles, pedestrians, and/or obstacles, etc. The computer vision system may use an object recognition algorithm, video tracking, and other computer vision techniques. In some embodiments, the computer vision system can map an environment, track objects, and estimate the speed of objects, etc. Perception module 302 can also detect objects based on other sensors data provided by other sensors such as a radar and/or LIDAR.

For each of the objects, prediction module 303 predicts what the object will behave under the circumstances. The prediction is performed based on the perception data perceiving the driving environment at the point in time in view of a set of map/rout information 311 and traffic rules 312. For example, if the object is a vehicle at an opposing direction and the current driving environment includes an intersection, prediction module 303 will predict whether the vehicle will likely move straight forward or make a turn. If the perception data indicates that the intersection has no traffic light, prediction module 303 may predict that the vehicle may have to fully stop prior to enter the intersection. If the perception data indicates that the vehicle is currently at a left-turn only lane or a right-turn only lane, prediction module 303 may predict that the vehicle will more likely make a left turn or right turn respectively.

For each of the objects, decision module 304 makes a decision regarding how to handle the object. For example, for a particular object (e.g., another vehicle in a crossing route) as well as its metadata describing the object (e.g., a speed, direction, turning angle), decision module 304 decides how to encounter the object (e.g., overtake, yield, stop, pass). Decision module 304 may make such decisions according to a set of rules such as traffic rules or driving rules 312, which may be stored in persistent storage device 352.

Routing module 307 is configured to provide one or more routes or paths from a starting point to a destination point. For a given trip from a start location to a destination location, for example, received from a user, routing module 307 obtains route and map information 311 and determines all possible routes or paths from the starting location to reach the destination location. Routing module 307 may generate a reference line in a form of a topographic map for each of the routes it determines from the starting location to reach the destination location. A reference line refers to an ideal route or path without any interference from others such as other vehicles, obstacles, or traffic condition. That is, if there is no other vehicle, pedestrians, or obstacles on the road, an ADV should exactly or closely follows the reference line. The topographic maps are then provided to decision module 304 and/or planning module 305. Decision module 304 and/or planning module 305 examine all of the possible routes to select and modify one of the most optimal routes in view of other data provided by other modules such as traffic conditions from localization module 301, driving environment perceived by perception module 302, and traffic condition predicted by prediction module 303. The actual path or route for controlling the ADV may be close to or different from the reference line provided by routing module 307 dependent upon the specific driving environment at the point in time.

Based on a decision for each of the objects perceived, planning module 305 plans a path or route for the autonomous vehicle, as well as driving parameters (e.g., distance, speed, and/or turning angle), using a reference line provided by routing module 307 as a basis. That is, for a given object, decision module 304 decides what to do with the object, while planning module 305 determines how to do it. For example, for a given object, decision module 304 may decide to pass the object, while planning module 305 may determine whether to pass on the left side or right side of the object. Planning and control data is generated by planning module 305 including information describing how vehicle 300 would move in a next moving cycle (e.g., next route/path segment). For example, the planning and control data may instruct vehicle 300 to move 10 meters at a speed of 30 mile per hour (mph), then change to a right lane at the speed of 25 mph.

As part of the planning process, the trajectory optimizer 308 may generate a plurality of planned ADV states based on a cost function 313, which may be stored in persistent storage device 352.

Based on the planning and control data, control module 306 controls and drives the autonomous vehicle, by sending proper commands or signals to vehicle control system 111, according to a route or path defined by the planning and control data. The planning and control data include sufficient information to drive the vehicle from a first point to a second point of a route or path using appropriate vehicle settings or driving parameters (e.g., throttle, braking, steering commands) at different points in time along the path or route.

In one embodiment, the planning phase is performed in a number of planning cycles, also referred to as driving cycles, such as, for example, in every time interval of 100 milliseconds (ms). For each of the planning cycles or driving cycles, one or more control commands will be issued based on the planning and control data. That is, for every 100 ms, planning module 305 plans a next route segment or path segment, for example, including a target position and the time required for the ADV to reach the target position. Alternatively, planning module 305 may further specify the specific speed, direction, and/or steering angle, etc. In one embodiment, planning module 305 plans a route segment or path segment for the next predetermined period of time such as 5 seconds. For each planning cycle, planning module 305 plans a target position for the current cycle (e.g., next 5 seconds) based on a target position planned in a previous cycle. Control module 306 then generates one or more control commands (e.g., throttle, brake, steering control commands) based on the planning and control data of the current cycle.

Note that decision module 304 and planning module 305 may be integrated as an integrated module. Decision module 304/planning module 305 may include a navigation system or functionalities of a navigation system to determine a driving path for the autonomous vehicle. For example, the navigation system may determine a series of speeds and directional headings to affect movement of the autonomous vehicle along a path that substantially avoids perceived obstacles while generally advancing the autonomous vehicle along a roadway-based path leading to an ultimate destination. The destination may be set according to user inputs via user interface system 113. The navigation system may update the driving path dynamically while the autonomous vehicle is in operation. The navigation system can incorporate data from a GPS system and one or more maps so as to determine the driving path for the autonomous vehicle.

The term of polynomial optimization or polynomial fit refers to the optimization of the shape of a curve (in this example, a trajectory) represented by a polynomial function (e.g., quintic or quartic polynomial functions), such that the curve is continuous along the curve a derivative at the joint of two adjacent segments is obtainable). In the field of autonomous driving, the polynomial curve from a starting point to an end point is divided into a number of segments (or pieces), each segment corresponding to a control point (or reference point). Such a segmented polynomial curve is referred to as a piecewise polynomial. When optimizing the piecewise polynomial, a set of joint constraints and a set of boundary constraints between two adjacent segments have to be satisfied, in addition to the set of initial state constraints and end state constraints,

The set of joint constraints includes positions (x, y), speed, heading direction, and acceleration of the adjacent segments have to be identical. For example, the ending position of a first segment (e.g., leading segment) and the starting position of a second segment (e.g., following segment) have to be identical or within a predetermined proximity. The speed, heading direction, and acceleration of the ending position of the first segment and the corresponding speed, heading direction, and acceleration of the starting position of the second segment have to be identical or within a predetermined range. In addition, each control point is associated with a predefined boundary (e.g., 0.2 meters left and right surrounding the control point). The polynomial curve has to go through each control point within its corresponding boundary. When these two set of constraints are satisfied during the optimization, the polynomial curve representing a trajectory should be smooth and continuous.

In one embodiment, trajectories are planned in an SL-coordinate system. The SL-coordinate system may be defined relative to the reference line. The longitudinal distance, or s-distance, represents the distance along the tangential direction of the reference line. Correspondingly, the lateral distance, or 1-distance, represents the distance perpendicular to the s-direction. The longitudinal dimension in the SL space represents a longitudinal distance of a particular object from a current location of the vehicle that is presumably drives along the reference line. The lateral dimension in the SL space represents the shortest distance between the object and the reference line at a particular time or location represented by the longitudinal dimension. Such a graph in the SL space is referred to as an SL graph. In one embodiment, the lateral distance may be simply defined as the distance from the reference line. Therefore, in addition to representation in the Cartesian coordinate system (XY plane), a vehicle pose (position) may be represented in the SL-coordinate system as an ordered pair (longitudinal pose “s-pose”, lateral pose “l-pose”), or simply (s, l), with respect to a reference line.

Referring to FIG. 4, a diagram 400 illustrating a vehicle pose under an SL-coordinate system under an XY plane according to one embodiment is shown. The vehicle 410 has a pose (x, y) in the 2D Cartesian coordinate system. Additionally, the vehicle 410 pose may also be represented as (s, l) under an SL-coordinate system defined with respect to a reference line 420.

In the SL-coordinate system, a vehicle may have an s-speed, or longitudinal speed, which is the speed along the tangential direction of the reference line, and can be represented as {dot over (s)}=ds/dt (i.e., the first derivative of s-pose with respect to time). The vehicle further has an s-acceleration, or longitudinal acceleration, which is the acceleration along the tangential direction of the reference line, and can be represented as {umlaut over (s)}=d{dot over (s)}/dt (i.e., the first derivative of s-speed with respect to time, or the second derivative of s-pose with respect to time). It should be appreciated that at any time instant, a state of the vehicle may be represented under the SL-coordinate system by a triplet (s, s, {umlaut over (s)}). Moreover, jerk of the vehicle may be represented as

_(i→i−1)=({umlaut over (s)}_(i)−{umlaut over (s)}_(i−1))/Δt. The meaning of i and At will be explained in detail below.

Further, in the SL-coordinate system, a lateral acceleration of the vehicle may be represented as {umlaut over (l)}=d²l/ds² (i.e., the second derivative of l-pose with respect to s-pose).

In one embodiment, the trajectory optimizer receives one or more inputs, and generates one or more optimization outputs under one or more constraints, where the optimization outputs are values of optimization variables that minimize the value of a cost function associated with one or more optimization objectives.

In one embodiment, inputs to the trajectory optimizer may comprise: 1) a trajectory time length T; 2) a time discretization resolution Δt; 3) a vehicle starting state (s₀, {dot over (s)}_(o), {umlaut over (s)}₀) (i.e., the vehicle state (s, {dot over (s)}, {umlaut over (s)}) at t=0); 4) a road shape function K(s); 5) a maximal jerk

_(max) (

_(max)>0); 6) a maximal lateral acceleration {umlaut over (d)}_(max)({umlaut over (d)}_(max)>0); and 5) a target vehicle ending state (s_(e), {dot over (s)}_(e), {umlaut over (s)}_(e)).

In different embodiments, the trajectory time length T may be 5 seconds, 8 seconds, or any other suitable time length. The time discretization Δt may be 100 ms, or any other suitable time. Further, it should be appreciated that if the target vehicle ending state is not used, s_(e) may be set to infinity (∞).

In one embodiment, the road shape function κ(s), which provides the curvature (i.e., the reciprocal of the radius, or 1/R) of the reference line at each s-position, may be a piecewise sequence of 4^(th) order (quartic) spiral curves. Each of the quartic spiral curve may be of the form κ(s)=as⁴+bs³+cs²+ds+e. Such a road shape function κ(s) may be generated by using a series of quartic spiral curves to connect consecutive, sparsely discretized points of the reference line. By using the quartic spiral curves, the curves are guaranteed to be smoothly connected at the joint points to the second order. This is desirable because constraints in an optimization need to be smooth—first order smoothness is required and second order smoothness is desirable. In conventional methods, the shape of the reference line is given by a sequence of densely discretized points, and a linear function is used for interpolation between the consecutive points. Such conventional, piecewise linear representation of the reference line leads to discontinuity in the first order derivative, and is therefore not suitable for use in the optimization.

The optimization variables may be the vehicle state (s, {dot over (s)}, {umlaut over (s)}) at each time discretization resolution Δt after the starting time up to the trajectory time length T, which corresponds to the planning ending time. In other words, the optimization variables may comprise: (s₁, {dot over (s)}₁, {umlaut over (s)}₁, (i.e., the vehicle state at t=1Δt), (s₂, {dot over (s)}₂, {umlaut over (s)}₂) (i.e., the vehicle state at t=2Δt), etc., including all the intervening vehicle states up to the ending state (s_(N), {dot over (s)}_(N), {umlaut over (s)}_(N)) (i.e., the vehicle state at t=T=NΔt).

In one embodiment, the trajectory optimizer operates under the following equality constraints: 1) ∀i∈[1,N] (for any i between 1 and N, inclusive),

_(i→i−1)=({umlaut over (s)}_(i)−{umlaut over (s)}_(i−1))/Δt; 2) ∀i−[1,N], _(i)={dot over (s)}_(i−1)+{umlaut over (s)}_(i−1)*Δt+1/2*

_(i→i−1)*Δt²; and 3) ∀i∈[1,N], s_(i)=s_(i−1)+{dot over (s)}_(i−1)*Δt+1/2*{umlaut over (s)}_(i−1)*Δt²+1/6*

_(i→i−1)*Δt³. It should be appreciated that the equality constraints 1) through 3) ensure that from one At to the next, the correct mathematical relationships among s_(i), {dot over (s)}_(i)

_(i″i−1), s_(i−1), and {dot over (s)}_(i−1) are maintained.

The trajectory optimizer further operates under the following inequality constraints: 1) ∀i∈[1,N],

_(i→i−1)∈[−

_(max),

_(max)], which ensures that the jerk

_(i→i−1) never exceeds the maximal jerk

_(max) in either direction; and 2) ∀i∈[1,N], {dot over (s)}_(i)*{dot over (s)}_(i)*κ(s_(i))∈[−{umlaut over (d)}_(max), {umlaut over (d)}_(max)], which ensures that the lateral acceleration never exceeds the maximal lateral acceleration {umlaut over (d)}_(max) in either direction.

In one embodiment, the cost function associated with the objectives and to be minimized may be w₀*Σ₁ ^(N)

_(i→i−1) ²+w₁*(s_(N)−s_(e))²+w₂*({dot over (s)}_(N)−{dot over (s)}_(e))+w₃*({umlaut over (s)}_(N)−{umlaut over (s)}_(e)), where w₀, w₁, w₂, and w₃ are weights that can be determined empirically. Therefore, it should be appreciated that by minimizing the cost function, the optimization yields, within the confines of the inputs and constraints, outputs that meet a number of goals: 1) minimizing cumulative jerk

_(i→i−1); 2) bringing the vehicle as close to the target end s-pose s_(e) at the end of the trajectory time length T as possible, or if no target end s-pose s_(e) is specified (i.e., set to infinity), as far along the tangential direction of the reference line as possible; 3) bringing the vehicle as close to the target end s-speed {dot over (s)}_(e) (e.g., a predetermine non-zero target s-speed, a zero target s-speed for e.g., a stop sign, or a same s-speed as that of a front vehicle) at the end of the trajectory time length T as possible; and 4) bringing the vehicle as close to the target end s-acceleration {umlaut over (s)}_(e) (e.g., zero target end-acceleration) at the end of the trajectory time length T as possible. The relative importance of these goals is controlled by the weights w₀, w₁ w₂, and w₃.

Referring to FIG. 5, a block diagram 500 illustrating various example components involved in the optimization process according to one embodiment is shown. In one embodiment, the trajectory optimizer 308 may be integrated into the planning module 305 of FIGS. 3A and 3B.The trajectory optimizer 308 receives inputs 520, constraints 530, optimization variables 540, and a cost function 313 associated with optimization objectives. The trajectory optimizer 308 performs nonlinear optimization, and yields optimization results 560, which are values of optimization variables 540 that minimize the value of the cost function 313. Nonlinear optimization is well-known in the art, and therefore is not described in further detail herein. The trajectory optimizer 308 may be implemented in hardware, software, or a combination of both.

Referring to FIG. 6, a flowchart illustrating an example method 600 for planning an optimal trajectory at an ADV according to one embodiment is shown. The method 600 may be performed by hardware, software, or a combination of both. At block 610, a plurality of optimization inputs may be received, the plurality of optimization inputs comprising a trajectory time length (T), a time discretization resolution (Δt), an autonomous driving vehicle (ADV) starting state, a road shape function (κ(s)), a maximal jerk, and a maximal lateral acceleration. At block 620, a plurality of optimization constraints may be received, the plurality of optimization constraints comprising constraints relating to the maximal jerk and the maximal lateral acceleration. At block 630, a cost function associated with an optimization objective may be received, the cost function comprising a first term relating to cumulative jerk, a second term relating to an end longitudinal position, a third term relating to an end longitudinal speed, and a fourth term relating to an end longitudinal acceleration. At block 640, a plurality of planned ADV states may be generated as optimization results with nonlinear optimization, wherein the optimization results minimize a value of the cost function. At block 650, control signals may be generated to control the ADV based on the plurality of planned ADV states.

In one embodiment, an SL-coordinate system comprising a longitudinal dimension and a lateral dimension may be utilized. The longitudinal (s) dimension is along a tangential direction of a reference line, and the lateral (l) dimension is perpendicular to the longitudinal dimension. Each of the ADV starting state and the plurality of planned ADV states may comprise a longitudinal position (s-pose), a longitudinal speed (s-speed), and a longitudinal acceleration (s-acceleration).

The road shape function may comprise a sequence of quartic spiral curves. The cost function may further comprise a first weight (w0) associated with the first term, a second weight (w1) associated with the second term, a third weight (w2) associated with the third term, and a fourth weight (w3) associated with the fourth term.

The plurality of planned ADV states may correspond to time instants spaced by the time discretization resolution (Δt) between a planning starting time (t=0) and a planning ending time (t=T), and wherein the planning ending time is later than the planning starting time by the trajectory time length (T). In one embodiment, the plurality of optimization inputs may further comprise a target ADV ending state.

Note that some or all of the components as shown and described above may be implemented in software, hardware, or a combination thereof. For example, such components can be implemented as software installed and stored in a persistent storage device, which can be loaded and executed in a memory by a processor (not shown) to carry out the processes or operations described throughout this application. Alternatively, such components can be implemented as executable code programmed or embedded into dedicated hardware such as an integrated circuit (e.g., an application specific IC or ASIC), a digital signal processor (DSP), or a field programmable gate array (FPGA), which can be accessed via a corresponding driver and/or operating system from an application. Furthermore, such components can be implemented as specific hardware logic in a processor or processor core as part of an instruction set accessible by a software component via one or more specific instructions.

FIG. 7 is a block diagram illustrating an example of a data processing system which may be used with one embodiment of the disclosure. For example, system 1500 may represent any of data processing systems described above performing any of the processes or methods described above, such as, for example, perception and planning system 110 or any of servers 103-104 of FIG. 1 and the trajectory optimizer 308 of FIG. 5. System 1500 can include many different components. These components can be implemented as integrated circuits (ICs), portions thereof, discrete electronic devices, or other modules adapted to a circuit board such as a motherboard or add-in card of the computer system, or as components otherwise incorporated within a chassis of the computer system.

Note also that system 1500 is intended to show a high level view of many components of the computer system. However, it is to be understood that additional components may be present in certain implementations and furthermore, different arrangement of the components shown may occur in other implementations. System 1500 may represent a desktop, a laptop, a tablet, a server, a mobile phone, a media player, a personal digital assistant (PDA), a Smartwatch, a personal communicator, a gaming device, a network router or hub, a wireless access point (AP) or repeater, a set-top box, or a combination thereof. Further, while only a single machine or system is illustrated, the term “machine” or “system” shall also be taken to include any collection of machines or systems that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein.

In one embodiment, system 1500 includes processor 1501, memory 1503, and devices 1505-1508 connected via a bus or an interconnect 1308. Processor 1501 may represent a single processor or multiple processors with a single processor core or multiple processor cores included therein. Processor 1501 may represent one or more general-purpose processors such as a microprocessor, a central processing unit (CPU), or the like. More particularly, processor 1501 may be a complex instruction set computing (CISC) microprocessor, reduced instruction set computing (RISC) microprocessor, very long instruction word (VLIW) microprocessor, or processor implementing other instruction sets, or processors implementing a combination of instruction sets. Processor 1501 may also be one or more special-purpose processors such as an application specific integrated circuit (ASIC), a cellular or baseband processor, a field programmable gate array (FPGA), a digital signal processor (DSP), a network processor, a graphics processor, a communications processor, a cryptographic processor, a co-processor, an embedded processor, or any other type of logic capable of processing instructions.

Processor 1501, which may be a low power multi-core processor socket such as an ultra-low voltage processor, may act as a main processing unit and central hub for communication with the various components of the system. Such processor can be implemented as a system on chip (SoC). Processor 1501 is configured to execute instructions for performing the operations and steps discussed herein. System 1500 may further include a graphics interface that communicates with optional graphics subsystem 1504, which may include a display controller, a graphics processor, and/or a display device.

Processor 1501 may communicate with memory 1503, which in one embodiment can be implemented via multiple memory devices to provide for a given amount of system memory. Memory 1503 may include one or more volatile storage (or memory) devices such as random access memory (RAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), static RAM (SRAM), or other types of storage devices. Memory 1503 may store information including sequences of instructions that are executed by processor 1501, or any other device. For example, executable code and/or data of a variety of operating systems, device drivers, firmware (e.g., input output basic system or BIOS), and/or applications can be loaded in memory 1503 and executed by processor 1501. An operating system can be any kind of operating systems, such as, for example, Robot Operating System (ROS), Windows® operating system from Microsoft®, Mac OS®/iOS® from Apple, Android® from Google®, LINUX, UNIX, or other real-time or embedded operating systems.

System 1500 may further include 10 devices such as devices 1505-1508, including network interface device(s) 1505, optional input device(s) 1506, and other optional 10 device(s) 1507. Network interface device 1505 may include a wireless transceiver and/or a network interface card (NIC). The wireless transceiver may be a WiFi transceiver, an infrared transceiver, a Bluetooth transceiver, a WiMax transceiver, a wireless cellular telephony transceiver, a satellite transceiver (e.g., a global positioning system (GPS) transceiver), or other radio frequency (RF) transceivers, or a combination thereof. The NIC may be an Ethernet card.

Input device(s) 1506 may include a mouse, a touch pad, a touch sensitive screen (which may be integrated with display device 1504), a pointer device such as a stylus, and/or a keyboard (e.g., physical keyboard or a virtual keyboard displayed as part of a touch sensitive screen). For example, input device 1506 may include a touch screen controller coupled to a touch screen. The touch screen and touch screen controller can, for example, detect contact and movement or break thereof using any of a plurality of touch sensitivity technologies, including but not limited to capacitive, resistive, infrared, and surface acoustic wave technologies, as well as other proximity sensor arrays or other elements for determining one or more points of contact with the touch screen.

TO devices 1507 may include an audio device. An audio device may include a speaker and/or a microphone to facilitate voice-enabled functions, such as voice recognition, voice replication, digital recording, and/or telephony functions. Other IO devices 1507 may further include universal serial bus (USB) port(s), parallel port(s), serial port(s), a printer, a network interface, a bus bridge (e.g., a PCI-PCI bridge), sensor(s) (e.g., a motion sensor such as an accelerometer, gyroscope, a magnetometer, a light sensor, compass, a proximity sensor, etc.), or a combination thereof. Devices 1507 may further include an imaging processing subsystem (e.g., a camera), which may include an optical sensor, such as a charged coupled device (CCD) or a complementary metal-oxide semiconductor (CMOS) optical sensor, utilized to facilitate camera functions, such as recording photographs and video clips. Certain sensors may be coupled to interconnect 1308 via a sensor hub (not shown), while other devices such as a keyboard or thermal sensor may be controlled by an embedded controller (not shown), dependent upon the specific configuration or design of system 1500.

To provide for persistent storage of information such as data, applications, one or more operating systems and so forth, a mass storage (not shown) may also couple to processor 1501. In various embodiments, to enable a thinner and lighter system design as well as to improve system responsiveness, this mass storage may be implemented via a solid state device (SSD). However in other embodiments, the mass storage may primarily be implemented using a hard disk drive (HDD) with a smaller amount of SSD storage to act as a SSD cache to enable non-volatile storage of context state and other such information during power down events so that a fast power up can occur on re-initiation of system activities. Also a flash device may be coupled to processor 1501, e.g., via a serial peripheral interface (SPI). This flash device may provide for non-volatile storage of system software, including BIOS as well as other firmware of the system.

Storage device 1508 may include computer-accessible storage medium 1509 (also known as a machine-readable storage medium or a computer-readable medium) on which is stored one or more sets of instructions or software (e.g., module, unit, and/or logic 1528) embodying any one or more of the methodologies or functions described herein. Processing module/unit/logic 1528 may represent any of the components described above, such as, for example, planning module 305, control module 306, and trajectory optimizer 308. Processing module/unit/logic 1528 may also reside, completely or at least partially, within memory 1503 and/or within processor 1501 during execution thereof by data processing system 1500, memory 1503 and processor 1501 also constituting machine-accessible storage media. Processing module/unit/logic 1528 may further be transmitted or received over a network via network interface device 1505.

Computer-readable storage medium 1509 may also be used to store the some software functionalities described above persistently. While computer-readable storage medium 1509 is shown in an exemplary embodiment to be a single medium, the term “computer-readable storage medium” should be taken to include a single medium or multiple media (e.g., a centralized or distributed database, and/or associated caches and servers) that store the one or more sets of instructions. The terms “computer-readable storage medium” shall also be taken to include any medium that is capable of storing or encoding a set of instructions for execution by the machine and that cause the machine to perform any one or more of the methodologies of the present disclosure. The term “computer-readable storage medium” shall accordingly be taken to include, but not be limited to, solid-state memories, and optical and magnetic media, or any other non-transitory machine-readable medium.

Processing module/unit/logic 1528, components and other features described herein can be implemented as discrete hardware components or integrated in the functionality of hardware components such as ASICS, FPGAs, DSPs or similar devices. In addition, processing module/unit/logic 1528 can be implemented as firmware or functional circuitry within hardware devices. Further, processing module/unit/logic 1528 can be implemented in any combination hardware devices and software components.

Note that while system 1500 is illustrated with various components of a data processing system, it is not intended to represent any particular architecture or manner of interconnecting the components; as such details are not germane to embodiments of the present disclosure. It will also be appreciated that network computers, handheld computers, mobile phones, servers, and/or other data processing systems which have fewer components or perhaps more components may also be used with embodiments of the disclosure.

Some portions of the preceding detailed descriptions have been presented in terms of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations are the ways used by those skilled in the data processing arts to most effectively convey the substance of their work to others skilled in the art. An algorithm is here, and generally, conceived to be a self-consistent sequence of operations leading to a desired result. The operations are those requiring physical manipulations of physical quantities.

It should be borne in mind, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise as apparent from the above discussion, it is appreciated that throughout the description, discussions utilizing terms such as those set forth in the claims below, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system's registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices.

Embodiments of the disclosure also relate to an apparatus for performing the operations herein. Such a computer program is stored in a non-transitory computer readable medium. A machine-readable medium includes any mechanism for storing information in a form readable by a machine (e.g., a computer). For example, a machine-readable (e.g., computer-readable) medium includes a machine (e.g., a computer) readable storage medium (e.g., read only memory (“ROM”), random access memory (“RAM”), magnetic disk storage media, optical storage media, flash memory devices).

The processes or methods depicted in the preceding figures may be performed by processing logic that comprises hardware (e.g. circuitry, dedicated logic, etc.), software (e.g., embodied on a non-transitory computer readable medium), or a combination of both. Although the processes or methods are described above in terms of some sequential operations, it should be appreciated that some of the operations described may be performed in a different order. Moreover, some operations may be performed in parallel rather than sequentially.

Embodiments of the present disclosure are not described with reference to any particular programming language. It will be appreciated that a variety of programming languages may be used to implement the teachings of embodiments of the disclosure as described herein.

In the foregoing specification, embodiments of the disclosure have been described with reference to specific exemplary embodiments thereof. It will be evident that various modifications may be made thereto without departing from the broader spirit and scope of the disclosure as set forth in the following claims. The specification and drawings are, accordingly, to be regarded in an illustrative sense rather than a restrictive sense. 

What is claimed is:
 1. A computer-implemented method, comprising: receiving a plurality of optimization inputs, the plurality of optimization inputs comprising a trajectory time length, a time discretization resolution, an autonomous driving vehicle (ADV) starting state, a road shape function, a maximal jerk, and a maximal lateral acceleration; receiving a plurality of optimization constraints, the plurality of optimization constraints comprising constraints relating to the maximal jerk and the maximal lateral acceleration; receiving a cost function associated with an optimization objective, the cost function comprising a first term relating to cumulative jerk, a second term relating to an end longitudinal position, a third term relating to an end longitudinal speed, and a fourth term relating to an end longitudinal acceleration; generating a plurality of planned ADV states as optimization results with nonlinear optimization, wherein the optimization results minimize a value of the cost function; and generating control signals to control the ADV based on the plurality of planned ADV states.
 2. The method of claim 1, wherein an SL-coordinate system comprising a longitudinal dimension and a lateral dimension is utilized, wherein the longitudinal dimension is along a tangential direction of a reference line, and wherein the lateral dimension is perpendicular to the longitudinal dimension.
 3. The method of claim 2, wherein each of the ADV starting state and the plurality of planned ADV states comprises a longitudinal pose, a longitudinal speed, and a longitudinal acceleration.
 4. The method of claim 2, wherein the road shape function comprises a sequence of quartic spiral curves.
 5. The method of claim 2, wherein the cost function further comprises a first weight associated with the first term, a second weight associated with the second term, a third weight associated with the third term, and a fourth weight associated with the fourth term.
 6. The method of claim 2, wherein the plurality of planned ADV states correspond to time instants spaced by the time discretization resolution between a planning starting time and a planning ending time, and wherein the planning ending time is later than the planning starting time by the trajectory time length.
 7. The method of claim 2, wherein the plurality of optimization inputs further comprise a target ADV ending state.
 8. A non-transitory machine-readable medium having instructions stored therein, which when executed by a processor, cause the processor to perform operations, the operations comprising: receiving a plurality of optimization inputs, the plurality of optimization inputs comprising a trajectory time length, a time discretization resolution, an autonomous driving vehicle (ADV) starting state, a road shape function, a maximal jerk, and a maximal lateral acceleration; receiving a plurality of optimization constraints, the plurality of optimization constraints comprising constraints relating to the maximal jerk and the maximal lateral acceleration; receiving a cost function associated with an optimization objective, the cost function comprising a first term relating to cumulative jerk, a second term relating to an end longitudinal position, a third term relating to an end longitudinal speed, and a fourth term relating to an end longitudinal acceleration; generating a plurality of planned ADV states as optimization results with nonlinear optimization, wherein the optimization results minimize a value of the cost function; and generating control signals to control the ADV based on the plurality of planned ADV states.
 9. The non-transitory machine-readable medium of claim 8, wherein an SL-coordinate system comprising a longitudinal dimension and a lateral dimension is utilized, wherein the longitudinal dimension is along a tangential direction of a reference line, and wherein the lateral dimension is perpendicular to the longitudinal dimension.
 10. The non-transitory machine-readable medium of claim 9, wherein each of the ADV starting state and the plurality of planned ADV states comprises a longitudinal pose, a longitudinal speed, and a longitudinal acceleration.
 11. The non-transitory machine-readable medium of claim 9, wherein the road shape function comprises a sequence of quartic spiral curves.
 12. The non-transitory machine-readable medium of claim 9, wherein the cost function further comprises a first weight associated with the first term, a second weight associated with the second term, a third weight associated with the third term, and a fourth weight associated with the fourth term.
 13. The non-transitory machine-readable medium of claim 9, wherein the plurality of planned ADV states correspond to time instants spaced by the time discretization resolution between a planning starting time and a planning ending time, and wherein the planning ending time is later than the planning starting time by the trajectory time length.
 14. The non-transitory machine-readable medium of claim 9, wherein the plurality of optimization inputs further comprise a target ADV ending state.
 15. A data processing system, comprising: a processor; and a memory coupled to the processor to store instructions, which when executed by the processor, cause the processor to perform operations, the operations including receiving a plurality of optimization inputs, the plurality of optimization inputs comprising a trajectory time length, a time discretization resolution, an autonomous driving vehicle (ADV) starting state, a road shape function, a maximal jerk, and a maximal lateral acceleration, receiving a plurality of optimization constraints, the plurality of optimization constraints comprising constraints relating to the maximal jerk and the maximal lateral acceleration, receiving a cost function associated with an optimization objective, the cost function comprising a first term relating to cumulative jerk, a second term relating to an end longitudinal position, a third term relating to an end longitudinal speed, and a fourth term relating to an end longitudinal acceleration, generating a plurality of planned ADV states as optimization results with nonlinear optimization, wherein the optimization results minimize a value of the cost function, and generating control signals to control the ADV based on the plurality of planned ADV states.
 16. The data processing system of claim 15, wherein an SL-coordinate system comprising a longitudinal dimension and a lateral dimension is utilized, wherein the longitudinal dimension is along a tangential direction of a reference line, and wherein the lateral dimension is perpendicular to the longitudinal dimension.
 17. The data processing system of claim 16, wherein each of the ADV starting state and the plurality of planned ADV states comprises a longitudinal pose, a longitudinal speed, and a longitudinal acceleration.
 18. The data processing system of claim 16, wherein the road shape function comprises a sequence of quartic spiral curves.
 19. The data processing system of claim 16, wherein the cost function further comprises a first weight associated with the first term, a second weight associated with the second term, a third weight associated with the third term, and a fourth weight associated with the fourth term.
 20. The data processing system of claim 16, wherein the plurality of planned ADV states correspond to time instants spaced by the time discretization resolution between a planning starting time and a planning ending time, and wherein the planning ending time is later than the planning starting time by the trajectory time length.
 21. The data processing system of claim 16, wherein the plurality of optimization inputs further comprise a target ADV ending state. 